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Search: id:A055879
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| A055879 |
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Least non-decreasing sequence with a(1) = 1 and Hankel transform {1,1,1,1,...}. |
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+0
5
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| 1, 1, 2, 2, 5, 5, 15, 15, 51, 51, 188, 188, 731, 731, 2950, 2950, 12235, 12235, 51822, 51822, 223191, 223191, 974427, 974427, 4302645, 4302645
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Hankel transform {t(n)} of {a(n)} is given by t(n) = Det[{a(1), a(2), ..., a(n)}, {a(2), a(3), ..., a(n+1)}, ..., {a(n), a(n+1), ..., a(2n-1)}].
The bisections of this sequence appear to be the binomial transform of the Catalan numbers, A007317. If that is true then the g.f. for this sequence is (1/(2*x))*( 1 + x - (1-x)^(-1)*(1-x^2)^(1/2)*(1-5*x^2)^(1/2)), which occurs in the Cyvin et al. reference.
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REFERENCES
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B. N. Cyvin et al., A class of polygonal systems representing polycyclic conjugated hydrocarbons ..., Monat. f. Chemie, 125 (1994), 1327-1337 (see V(x)).
S. J. Cyvin et al., "Enumeration and classification of certain polygonal systems representing polycyclic conjugated hydrocarbons: annelated catafusenes", J. Chem. Inf. Comput. Sci., 34 (1994), 1174-1180. See Table 1 second column on page 1174.
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LINKS
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J. W. Layman, The Hankel Transform and Some of its Properties, J. Integer Sequences, 4 (2001), #01.1.5.
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CROSSREFS
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Adjacent sequences: A055876 A055877 A055878 this_sequence A055880 A055881 A055882
Sequence in context: A106181 A098887 A097438 this_sequence A056470 A056471 A083849
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Jul 15 2000
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